ABC | Volume 113, Nº4, October 2019

Original Article Sánchez-Hechavarría et al. Inequality in HRV spectrum for evaluation of mental stress Arq Bras Cardiol. 2019; 113(4):725-733 income inequality is maximal and the Gini coefficient is equal to 1. 25,,26 Kyung-Jin You et al., 26 in 2016, have proposed the Gini coefficient to quantify the inequality in the power spectrum in the range of interest ( – Hz) in electroencephalography for quantifying the depth of consciousness during anesthesia. Applying this to HRV, if each frequency of the power spectrum of the RR intervals is considered as an individual house and the power of the corresponding frequency is considered as the house income, it would be possible to quantify the spectral inequality in terms of the Gini coefficient. Therefore, the Spectral Gini coefficient (SpG) is expressed as: = SpG Hz – Σ H = L X ( ) 2(H – L + 1) Σ = 1 Σ = 1 X ( ) – X ( ) The SpG can measure the inequality in the spectral powers of the RR intervals in each spectral HRV bands employed. Statistical analysis All values were expressed as Mean (X), Standard Deviation (SD) and Coefficient of Variation (CV %), Median [*] and Interquartile Range [¥]. All differences were considered statistically significant for p < 0.05. TheWilcoxon Signed-Rank Test (non-parametric test) for two related samples was used to compare rest versus mental stress. Effect Size with Gates’ delta was calculated and values above 0.80 were adopted with high magnitude. 27 In order to verify the association between traditional and Spectral Gini indices of HRV during mental stress and rest, Pearson’s correlation was applied to the data with normal distribution, or Spearman’s correlation, for the ones that did not accept this distribution. The normality of the data was initially determined using the Shapiro-Wilk test. Principal Component Analysis (PCA) is a technique to reduce the dimensionality of data consisting of correlated variables while capturing the bulk of variation present in the data. 28 There are as many principal components (PCs) as there are original variables. Each PC is a linear combination of the original variables with a set of weights called “loadings”, which reflect the correlations between PCs and original variables. PC1 is the directional vector representing the best fit for data cloud. PC2 is the directional vector orthogonal to PC1 that provides the best fit for residual variability in the data, and so on. PCs are mutually uncorrelated. Effective dimensionality reduction is achieved when the first few (dominant) PCs capture most of the variation present in the data. Useful insights on the interrelationship between original variables can be obtained when the dominant PCs have substantive interpretations. The efficacy of the traditional and Spectral Gini Indices of HRV were defined by the Receiver Operating Characteristic (ROC) curve through Sensitivity, Specificity, Area Under Curve and its respective p value were used with Cutoff Points between rest and mental stress set by Youden Index. All the statistical and mathematical calculations, as well as the processing of the signals, were performed using the Matlab 2012b software. Results Table 1 describes values of traditional and Spectral Gini Indices of HRV at rest and during mental stress. There was a significant decrease in HF (p = 0.046), a significant increase in the heart rate (p = 0.004), LF/HF (p = 0.002), LF (p = 0.033) and LF2 (p = 0.019) during mental stress, compared to rest. A significant increase in SpG(LF) (p = 0.009) and SpG(LF2) (p = 0.033) was observed. Coefficient of Variation analysis showed that Spectral Gini Indices are more homogeneous than traditional Indices of HRV. The correlation values between traditional and Spectral Gini Indices of HRV during rest and mental stress are shown in Table 2. During rest, there were high correlations between the HR and the SpG(LF1) (r = 0.721; p = 0.01) and between SpG(LF) and SpG(LF2) (r=0.829; p = 0.01), good correlations between LF and SpG(LF2) (r = 0.645; 0.05), and between LF2 and SpG(LF2) (r = 0.628; 0.05). During mental stress, there was a good correlation between SpG(LF) and SpG(LF2) (r = 0.682; 0.05). Figure 1 and Table 3 represent Principal Component Analysis (PCA) of Traditional and Spectral Gini Indices of Heart Rate Variability during rest and mental stress. The PCA helps to reduce the multiple characteristics or variables of a sample to a few dimensions (in this case, only two dimensions). It can be explained as trying to reduce twelve variables of an object to two values or characteristics and to determine which out of these twelve variables are the most robust for those two characteristics (two dimensions), which allow a better study of the object of interest. The important variables for each dimension are those that are higher than 1 or lower than -1. On dimension 1, the variables LF (1.4742), HF (1.2896), LF1 (1.4674) and LF2 (1.3519) have greater weight. On dimension 2, the variables with a greater load are HR (1.3612), LF/HF (1.2657), SpG LF (1.4026) and SpG LF2 (1.0909). With respect to Figure 1, the relationship between the variables is given by the cosine of the angle formed by each vector representing that specific variable. The more acute the angle, which is to say that it has a tendency to 0, the higher will be correlation, and if the vectors form a 90 degree angle, the variables will not be correlated. On the other hand, if they form an angle of 180 degrees, correlation is inverse. In dimension 2, the vectors of the variables HR, LF/HF and SpG LF form an angle close to 180 with the EDR and therefore, HR, LF/HF and SpG LF are negatively correlated with EDR. The size of the vector is the strength of that variable in that dimension. Discussion The present study aimed 1) to apply the Gini coefficient to power spectral densities of HRV to measure the inequality in distribution of frequency bands; 2) to compare the inequality in power spectrum of HRV signals during rest versus under mental stress; 3) to evaluate the Gini coefficient as a psychophysiological indicator of mental stress in comparison to traditional HRV indices. In the present study, the traditional indices of HRV during mental stress showed expected results of significant increase in LF power and increase in LF/HF ratio, along with significant decrease in HF power. HRV is a reliable tool to measure psychophysiological stress 29 and the present results shows significant changes in HRV indices compared to rest. 727